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Chapter 10 Practical Geometry Ex 10.4 Solutions

Question - 1 : - Construct тИЖABC, given m тИаA = 60┬░, m тИаB = 30┬░ and AB = 5.8 cm.

Answer - 1 : -

Steps of construction:
(i) Draw AB = 5.8 cm.
(ii) Draw тИаA = 60┬░ and тИаB = 30┬░ to meet each other at C.
(iii) ABC is the required triangle.
Using ASA criterion

Question - 2 : -
Construct тИЖPQR if PQ = 5 cm, m тИаPQR = 105┬░ and mтИаQRP = 40┬░.
(Hint: Recall angle-sum property of a triangle)

Answer - 2 : -

Given: mтИаPQR = 40┬░, mтИаQRP = 105┬░
тИ╡ mтИаPQR + mтИаQRP + тИаQPR = 180┬░ (Angle sum property of a triangle)
105┬░ + 40┬░ + тИаQPR = 180┬░
145┬░ + тИаQPR = 180┬░
тИ┤ тИаQPR = 180┬░ тАУ 145┬░ = 35┬░
┬а
Steps of construction:
(i) Draw PQ = 5 cm.
(ii) Draw тИаQPR = 35┬░ and тИаPQR = 40┬░ to meet each other at R.
(iii) тИЖPQR is the required triangle.
[Using AAS or ASA criterion]

Question - 3 : - Examine whether you can construct тИЖDEF such that EF = 7.2 cm, mтИаE = 110┬░ and mтИаF = 80┬░. Justify your answer.

Answer - 3 : -

To construct тИЖDEF with the given measurement, is not possible.
тИ╡ mтИаE + mтИаF = 110┬░ + 80┬░
= 190┬░ > 180┬░ [Sum of the angles of a triangle = 180┬░]
тИ┤ ADEF is not possible to construct.

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